An amplitude-phase (Ermakov-Lewis) approach for the Jackiw-Pi model of bilayer graphene

Abstract

In the context of bilayer graphene we use the simple gauge model of Jackiw and Pi to construct its numerical solutions in powers of the bias potential V according to a general scheme due to Kravchenko. Next, using this numerical solutions, we develop the Ermakov-Lewis approach for the same model. This leads us to numerical calculations of the Lewis-Riesenfeld phases that could be of forthcoming experimental interest for bilayer graphene. We also present a generalization of the Ioffe-Korsch nonlinear Darboux transformation

arXiv commentFTC, 11 pp, 5 figures

References in corpus (7)

• Electric Field Effect in Atomically Thin Carbon Films
• Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Electron fractionalization in two-dimensional graphenelike structures
• Chiral Gauge Theory for Graphene
• Persistence of zero modes in a gauged Dirac model for bilayer graphene
• Nonlinear Supersymmetric (Darboux) Covariance of the Ermakov-Milne-Pinney Equation

Cited by in corpus (7)

• Transmutations and spectral parameter power series in eigenvalue problems
• Transmutations for Darboux transformed operators with applications
• Spectral parameter power series representation for Hill's discriminant
• Complete systems of recursive integrals and Taylor series for solutions of Sturm-Liouville equations
• A finite-sum representation for solutions for the Jacobi operator
• Integral representation for scattering phase shifts via the phase-amplitude approach
• Noether symmetries and conservation laws of a reduced gauged bilayer graphene model